Hydrostatic Pressure

bob_46

This image helped me when I first tried to get my head around the principle

Bob Gagnon plumbing and heating

Hydrostatic Pressure

One foot of water height will exert 2.31 lbs of pressure on the walls of the tank, is that 2.31 pounds per square inch, or just 2.31 lbs pressure on the whole wall?

Thanks, Bob Gagnon

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Larry C_13

unit of pressure is pounds per square inch.

It would be per square inch.

Imagine the wind blowing against the open swing out window. The wind is exerting 0.1 psi pressure. The window area being 5 square feet will require 72 pounds of force to close.

Imagine the same wind blowing against a full size door of 20 square feet. The door will require 288 pounds of force to close it.

Its the same pressure but four times the area. The force required is dependent on the pressure AND the area.

Another analogy is electrical. Pressure is like Voltage, Area is like Current, and the total Force is like Power. Volts time Amps equals Watts. Pressure times Area equals Force. Double the Voltage and halve the Amps and you still have the same Power. Double the Pressure and halve the Area and it still is the same total Force.

Larry C

Jamie Hall

It's never as easy as it looks, though, Bob...

First off, it's 1/2.31 psi at a foot of depth or about 0.43 psi per foot. If the tank is open or unpressurized at the top, the water at the top exerts zero pressure, and the pressure increases linearly as you go down. So at one foot it's 0.43 pounds per square inch, two feet 0.86 psi, and so on. If the tank is say 2 feet deep, the pressure on the bottom is the same all the way across -- 0.86 psi. So if you have a tank say a foot square (just to keep the math within reason!) that has an area of 144 square inches, and the force on the bottom is the pressure -- 4.62 psi -- times the area, or about 124 pounds.

Unknown

Tension in tank wall?

This is something I have always wondered about. Say you have a round open tank as in your example. What is the tensile stress in the wall? In other words, how much force is there on each linear inch of the vertical wall seam, trying to pull it apart? It will be a function of height as is the pressure, but how do you calculate it?

From the larger area involved, I would imagine there would be a larger tension on a larger diameter tank wall than a smaller one.

I always think about this when I look at the wall seam of my kid's backyard pool and notice there are more fasteners at the bottom!

scrook_2

tank wall stress

for a thin walled cylinder (such as a vertical tank or a copper tube) the tangential (or circumferential) stress = p*D/2*t where p is pressure, D is inside diameter, and t is wall thickness. Note units must be consistant, e.g. lb/inch^2, inches, & inches.

For example, a 14" diameter, 1/10" (~12 gauge steel) expansion tank at 12 psi (assume almost all air, almost no water in it so negligible hydrostatic effects) has tangential stress in the cylindrical walls of the steel of (12lb/in^2)*(14in)/(2*0.10in)= 840 lb/in^2 while 12 lb/in^2 of pressure is exerted against its inner walls.

If the diameter is doubled but the thickness remains unchanged then the stresses in the cylinder walls double (1680 psi) while the pressure *on* the inner walls remains 12 psi

If it's a closed/capped pressurized tank or a pressurized tube or pipe, the longitudinal stress = p*D/4*t (half the tangential stress). That's why an over-pressurized cylinder always splits on the length axis, not around the circumference.

It gets more complicated for thick walled tubes/pipes/etc., (say a 1/2" sch 80 iron pipe), but for many cases the thin wall case is close enough.

The Boiler Dr.

I thought it was the reverse

2.31 feet or 28" of water column equals 1 PSI the area does not matter - 1" or 100" square or round
If the level remains constant @ 2.31 feet the pressure will be the same wherever it is measured at the bottom of the resevoir.
If dealing with a large resevoir, now you need to factor the weight per unit of measure (gallon) of fluid contained in that resevoir. However, the downward force (ground pressure) measured in (pound,kg) will increase as a result of the contained volume
Just my .02546c (US converted to CDN)

The Boiler Dr.

Yep

pretty much what I thought and put in print Thanks